The idea to publish a Landolt-Börnstein volume solely devoted to the Fundamental Constants and the Physical and Chemical Units arose during the preparation of a symposium on "Metrology in Physics" held at the Physikalisch-Technische Bundesanstalt in Braunschweig, Germany. It was felt that such a volume could be very useful from many viewpoints. Precision measurement is of crucial importance for the progress of modern science and technology, and "Metrology", the art of performing precise measurements has become a widely acknowledged area of truly interdisciplinary character. The significance of the fundamental constants for the understanding of physics is by now well accepted, their use for the realization of the physical and chemical units being undoubted. The amount of available information turned out to be so substantial that the volume had to be split into two subvolumes. The present subvolume a covers the physical and chemical units, their description as well as the measuring principles and precision experimental techniques. In subvolume b which will follow shortly the status of the determination of the fundamental constants is summarized.